Unlabeled cells and tissues are transparent under visible light and, as such, can be approximated as phase objects, with a transmission function of the form t(x, y)≅A exp[iφ(x, y)]. That is to say that an intensity image, as rendered by a bright field microscope, loses the phase information and yields negligible contrast, since the intensity is the square modulus of the amplitude, which is to say that it is independent of φ(x, y). Much of light microscopy's four-century history has been shaped by the quest to develop new contrast mechanisms. Generating exogenous contrast requires designing new chemical compounds (e.g., dyes, fluorophores, nanoparticles) that bind to particular structures of interest and also absorb, emit, or scatter light significantly, basically converting the structure from a phase to an amplitude object.
On the other hand, intrinsic contrast methods exploit the light-tissue interaction in such a way as to couple the information carried by the phase into the final intensity image. These techniques do not aim to provide quantitative information about the optical thickness of the specimen. Instead, they provide non-invasive, label-free access to microscopic structures of cells and tissues, without the restrictions associated with exogenous contrast agents. While a number of methods utilizing intrinsic contrast have been proposed in recent years, the most commonly used label-free methods are phase contrast (PC) microscopy and differential interference contrast (DIC) microscopy, both of which have played major roles in biological investigations over the course of several decades.
A drawback of the forgoing methods is that each suffers from optical artifacts: halos in the case of PC, and directional shadows, in the case of DIC. In particular, DIC provides an intensity image that is related to the gradient of the field. Thus, using birefringent optics, two identical replicas of the image field, slightly shifted transversely, are produced at the observation plane,
                                                                                             I                  ⁡                                      (                                          x                      ,                      y                                        )                                                  =                                ⁢                                  A                  ⁢                                                                                                                                    ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                                                          ϕ                              ⁡                                                              (                                                                  x                                  ,                                  y                                                                )                                                                                                                                    +                                                  ⅇ                                                      ⅈ                            ⁢                                                                                                                  ⁢                                                          ⌊                                                                                                ϕ                                  ⁡                                                                      (                                                                                                                  x                                        +                                                                                  δ                                          ⁢                                                                                                                                                                          ⁢                                          x                                                                                                                    ,                                      y                                                                        )                                                                                                  +                                α                                                            ⌋                                                                                                                                                                  2                                                                                                                          =                                ⁢                                  2                  ⁢                                                                          ⁢                  A                  ⁢                                                            {                                              1                        +                                                  cos                          ⁡                                                      [                                                                                          δ                                ⁢                                                                                                                                  ⁢                                                                                                      ϕ                                    x                                                                    ⁡                                                                      (                                                                          x                                      ,                                      y                                                                        )                                                                                                                              +                              α                                                        ]                                                                                              }                                        .                                                                                                            (          1          )                    
In Eq. 1, I is the image intensity, φ the phase of the object, δx is the transverse shift between the two images, α is a controllable phase shift between the two fields, and the phase shift between the two fields, δφ, is proportional to the one-dimensional gradient of the phase φ,
                                                                                             δ                  ⁢                                                                          ⁢                                                            ϕ                      x                                        ⁡                                          (                                              x                        ,                        y                                            )                                                                      =                                ⁢                                                      ϕ                    ⁡                                          (                                                                        x                          +                                                      δ                            ⁢                                                                                                                  ⁢                            x                                                                          ,                        y                                            )                                                        -                                      ϕ                    ⁡                                          (                                              x                        ,                        y                                            )                                                                                                                                              ∝                                ⁢                                                                            ∂                                              ϕ                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                                            ∂                      x                                                        .                                                                                          (          2          )                    
DIC derives its power in revealing fine details in the specimen by virtue of the fact that adjusting α to a value of −π/2, transforms the cosine in Eq. 1 into a sine, which, in the limit of small values of δφ, becomes proportional to the one-dimensional gradient of the phase, since sin [δφx(x, y)]≅δφx(x, y). Insofar as DIC is highly sensitive to edges, it renders beautiful images of fibrous structures, for example. However, its limitation comes from the fact that the first order derivative changes sign rapidly across an edge, thereby generating spurious bright and dark regions (“shadowing”) along the direction of the gradient.
Use of grating as a diffractive optical element (DOE) for filtering at the back focal plane of an objective of a bright field microscope has been demonstrated by McIntyre et al., Differential interference contrast imaging using a spatial light modulator, Opt. Lett., vol. 34, pp. 2988-90 (2009) by taking the two first-order diffracted field, shifted, by two different distances, from the DC field, due to two different grating periods.
Spatial Light Interference Microscopy (SLIM) is a modality that provides quantitative phase imaging (QPI), distinguishing it as a technique with respect to PC and DIC, both of which provide only qualitative phase images of phase objects. SLIM is described, for example, in US Published Patent Application 2009/0290156 (to Popescu et al.) and by Wang et al., Spatial Light Interference Microscopy (SLIM), Opt. Exp., 19, pp. 1016-26 (2011), both of which are incorporated herein by reference. SLIM acquires an image of the quantitative phase delay of the optical path through the specimen albeit at the price in time and computation of successively interposing known phase delays with respect to a reference beam. Wang et al., Label-free intracellular transport measured by spatial light interference microscopy, J. Biomed. Opt., 16, 026019 (2011), incorporated herein by reference, describes benefits of applying a Laplace derivative operator to the digital data derived from the SLIM imaging technique, in particular, a highlighting of detail without introducing gradient artifacts at edges.
A method for highlighting fine detail in phase images without incurring the spurious shadowing that arises in DIC, and without the temporal delay and computational overhead of SLIM, would thus be highly desirable.